Sir Isaac Newton's mathematick philosophy more easily demonstrated: with Dr. Halley's account of comets illustrated. Being forty lectures read in the publick schools at Cambridge / By William Whiston ... For the use of the young students there. In this English edition ... corrected and improved by the author.
- William Whiston
- Date:
- 1716
Licence: Public Domain Mark
Credit: Sir Isaac Newton's mathematick philosophy more easily demonstrated: with Dr. Halley's account of comets illustrated. Being forty lectures read in the publick schools at Cambridge / By William Whiston ... For the use of the young students there. In this English edition ... corrected and improved by the author. Source: Wellcome Collection.
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![Diftance HI, divers Species of Ellipfes will be defcribed. But then, if the Length of the Thread fhall be increas'd or diminifh’d , in the fame Pro- portion as the Diftance of the Points H and I fhall be increas'd or diminifh’d, there will be de- fcrib'd indeed divers Ellipfes, but which are all of the fame Species, or like to one another, From whence it appears, that Ellipfes are not only in- numerable in Magnirude but in Species alfo, and reach from a Circle to a Right Line: For like as when the Points H and I meet together, the Ellip- fis becomes a Circle; fo when they are removd - from each other half the Length of the Thread, it becomes a Right Line, both Sides meeting to- gether. From whence alfo it is manifeft, that every Species of Ellipfes is no lefs different from any other, than che Extremes of them are diffe- rent on this Side from a Circle, and on that from a Right Line. It alfo appears from this Delinea- tion, that if from a Point taken at Pleafure in the Elliptick Periphery, as che Point B, you draw two Lines to the two Central Points ; thefe two Lines BH and BI taken together, will be equal to the greateft Diameter DK ;. and confequently that the Sum of them is always given: Which thing the Conítru&ion it felf fhews. For that Part of the Thread, which is extended from I to B, and from thence back to H, is the fame with that which returneth from I to F, and from thence back to H ; and again, that Part of the Thread which reaches from D to H, is the fame with that which reacheth from K to I, or DH is equal to. | IK ; therefore IB -j- BH, which by. the former is equal co ID -]- DH, is equal to. ID 4- IK, that js, to KD. d | And thus much for the Production of the Fi- 5$ qr» Lo](https://iiif.wellcomecollection.org/image/b30534744_0018.jp2/full/800%2C/0/default.jpg)
